Migrating from Eastern Europe to the UK or Ireland?

I have a BSc in computer science. How difficult will it be for me to find a job over the Internet and migrate to either the UK or Ireland.

I need a work permit to work in the EU.

It depends wether you are a citizien of a state belonging to eu, or not.
If your country belongs to eu, you don't need any permission.
If not it is different from country to country; each one has its own legislation about immigration, in Italy for ex. is very tought to obtain permissions.

Since you look for a job over the internet it shouldn't be so hard for you to be assumed in a work place.
Bye